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Materi Fisika Listrik 3 Kapasitansi

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  • Pengertian KapasitorPengertian Kapasitor Dua penghantar (plat) berdekatan yang diberi

    muatan sama tetapi berlawanan jenis disebut kapasitor.

    Sifat menyimpan energi listrik / muatan listrik. Kapasitas suatu kapasitor (C) ditentukan oleh Kapasitas suatu kapasitor (C) ditentukan oleh

    perbandingan antara besar muatan Q dari salah satu penghantarnya dengan beda potensial Vsatu penghantarnya dengan beda potensial Vantara kedua penghantar itu.

  • Kegunaan KapasitorU k hi d i j di l li ik d Untuk menghindari terjadinya loncatan listrik pada rangkaian2 yang mengandung kumparan bila tiba2 diputuskan arusnya.diputuskan arusnya.

    Rangkaian yang dipakai untuk menghidupkan mesin mobil

    Untuk memilih panjang gelombang yang ditangkap oleh pesawat penerima radio.

    Bentuk kapasitor Kapasitor bentuk keping sejajar Kapasitor bentuk keping sejajar Kapasitor bentuk bola sepusat Kapasitor bentuk silinderKapasitor bentuk silinder

  • MacamMacam--Macam KapasitorMacam Kapasitor

    Capacitor:Capacitor:Capacitor:Capacitor:A Device to Store EnergyStore Energy in the Form of an Electrican Electric Field

  • KapasitansiKapasitansi C adalah jumlah muatan yang disimpan dibagi dengan tegangandisimpan dibagi dengan tegangan

    Q = CV

    Satuan untuk kapasitansi

    Q CV

    Satuan untuk kapasitansi

    Coulomb/Volt = FaradCoulomb/Volt Farad

  • Capacitanceh f hthe amount of charge

    stored divided bythe voltage is thethe voltage is the capacitance C

    unit of capacitanceQ = CV

    unit of capacitance Coulomb/Volt = Farad

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  • Kapasitor Pelat Paralel Dua pelat paralel yang luasDua pelat paralel yang luas luas A jarak antar pelat d jarak antar pelat d kerapatan muatan sama ttp berbeda tanda

    C Q/Vd

    C = Q/V= A/(d/0)d A/(d/0)

    C = 0A/d 0Untuk menaikkan nilai kapasitansi

    b k l

    + membesarkan luasanmemperkecil celah

  • Bila ukuran ke dua pelat cukup besardibanding jarak celah d Edibanding jarak celah d

    Medan diantara ke dua pelat mempunyai nilai seragam

    E = /E = /0Beda potensial diantarak d l V = Ed = d/0

    +

    ke dua pelat V Ed d/0C = Q/V = Q/(Q/4 R) = 4 RC = Q/V = Q/(Q/40 R) = 40 R

    Kapasitansi bergantung pada bentuk geometri dariKapasitansi bergantung pada bentuk geometri dari permukaan.

  • Capacitance Depends onp p

    Separation of the plates (d) [d in m]Separation of the plates (d) [d in m]

    d1C d

    Plate Area (A) [A in m2]AC

    Dielectric Constant () [ in C2/N-m2]C

    ( ) [ / ]

  • Show Demo Model, calculate its capacitance , and showhow to charge it up with a battery.

    Circular parallel plate capacitor

    r = 10 cm

    g p y

    r r

    s

    A = r2 = (.1)2A = .03 m 2

    S = 1 mm = .001 m

    SAC 0=

    S

    001.03.)10( 11=C }Farad

    VoltCoulomb

    FC 10103 =

    pFC 300= p = pico = 10-12

  • 1. Consider two plates separated by d=1.5 cm , where the electric field between them is 100 V/m and the charge onelectric field between them is 100 V/m, and the charge on the plates is 30.0 C. What is the capacitance?

    The Capacitance is:The Capacitance is:2.0 10-5 F Or 20 microfarad.

    2. What is the capacitance of a capacitor if the charge is 0 075 C held at V = 400 V0.075 C held at V = 400 V

    C = Q/V =0.075 C/400 V= 1.875 X 10-4 f = 187.5 F

  • Dielectrics K Capacitors are usually constructed with an

    insulating material between the plates This helps prevent a breakdown or arcing This helps prevent a breakdown or arcing

    between the plates at higher voltages The plates can be placed closer together withoutThe plates can be placed closer together without

    danger of touching reducing d The capacitance is increased by a factor K

    (dielectric constant) The formula for capacitance is now

    C = K0 Ad0 d

  • Permitivitas Dielektrik = K0K adalah konstanta dielektrik

    tergantung pada material dielektrik g g pumumnya nilai K = 1 sampai 10

    Bila dielektrik sepenuhnya mengisi volume diantara pelat-pelat :

    E berkurang oleh faktor K E = / = /K E berkurang oleh faktor K E = / = /K0 V berkurang oleh faktor K V = d/K V berkurang oleh faktor K V = d/K0 C meningkat oleh faktor K C = K A/d C meningkat oleh faktor K C = K0A/d

  • Material KVacuum 1.00000Gl 5 10Glass 5-10Mica 3-6Mylar 3.1P ffi W 2 1 2 5Paraffin Wax 2.1 2.5Plexiglas 3.40Polyethylene 2.25P l i l hl id 3 18Polyvinyl chloride 3.18

    Teflon 2.1Porcelain 6.0 8.0

    Germanium 16Rubber 2.5 3.0

    Water 80 4Water 80.4Glycerin 42.5Liquid ammonia(-78C) 25Benzene 2 284Benzene 2.284Air(1 atm) 1.00059Air(100 atm) 1.0548

  • Question: The energy content of a charged capacitor resides in itsin its

    (a) plates (b) potential difference(c) charge (d) electric field

    Answer: d

    Question: The plates of a parallel-plate capacitor of capacitance C are brought together to one-third their original separation. The capacitance is now

    (a) C/9( )(b) C/3(c) 3C(d) 9C(d) 9C

    Answer: c

  • Examplep Two rectangular sheets of copper foil 16 X 20 cm are

    separated by a thin layer of paraffin wax 0 2 mm thickseparated by a thin layer of paraffin wax 0.2 mm thick. Calculate the capacitance if the dielectric constant for the wax is 2.4.

    dAKC o=

    m10X2mm2.0dm032.0cm320)cm20)(cm16(A

    4

    22

    =====

    pf3400f10X43Cm10X2

    )m032.0)(4.2)(Nm/C10X854.8(C

    9

    4

    22212

    =

    pf3400f10X4.3C ==

  • Energy Storage in CapacitorsEnergy Storage in Capacitors

    The energy stored in a capacitor is just theThe energy stored in a capacitor is just the work necessary to separate the charges in the first place.p

    As you keep moving charges, you have a greater force to overcome because the gpotential keeps increasing

    The total work is just the total charge times j gthe average voltage or W = QV/2.

  • Energy Storage in CapacitorsTotal charge stored on capacitor

    0

    Q

    W = V dq V = q / CTotal charge stored on capacitor

    0

    W ( /C)d Q2/2CQ1 Q

    0W = (q/C)dq = Q2/2C

    Energy = 12

    QV

    Q CVQVCVW 21

    221 ==

    Q =CVE U 1 CV 2 1 Q

    2Energy =U =

    2CV 2 =

    2QC

  • where is the energy located?

    W = C V2/2 = C (E d)2/2

    = (0 A / d) E2 d2 / 2 ( 0 )= (0 E2/2)(A d)= (energy density)(volume) (energy density)(volume)

    0E2/2 is the energy density0the energy is where the electric field is

    between the plates

    Misal kapasitor 1.2 F diberi muatan hingga berpotensial 3 kV, berapa energi yang tersimpan didalamnya?

    QVCVW 21221 == W = 5.4 Joule

  • Hubungan paralel kapasitorcc

    Parallel:V bernilai samauntuk ke dua kapasitor.Kapasitansi tinggal di jumlahkanjumlahkan.

    Ceq = Qtotal/VCeq = Q1/V1 + Q2/V2V = V = VV1 = V2 = VCeq = C1 + C2

  • Hubungan Paralel Kapasitor

    ; ; ; ; 332211 VCQVCQVCQVCQ p====

    321 CCCCp ++=

    Kapasitor yang dihubungkan paralel, tegangan antara ujung2 kapasitor adalah sama, sebesar V.ujung kapas tor adalah sama, sebesar V.

  • Hubungan seri kapasitor

    Seri : V tidak sama pada masing2Seri : V tidak sama pada masing2 kapasitor. Tetapi Q sama (mengapa?)

    1/ Ceq = V1/ Q1 + V2/ Q2qQ1 = Q2 = Q1/ Ceq = 1/ C1 + 1/ C2

  • Hubungan seri kapasitor

    adcdbcab CQV

    CQV

    CQV

    CQV ==== ; ; ;

    1111CCCC

    ++=sCCCC 321

    Kapasitor yang dihubungkan seri akan mempunyai

    321 CCCCs

    Kapasitor yang dihubungkan seri akan mempunyai muatan yang sama.

    321 QQQQ ===

  • Dua kapasitor dihubungkan seri yang dihubungkan dengan sumber 1000 V. Tentukan:

    a. C-subsitusi (gabungan)b. Muatan masing-masing kapasitorc. Beda potensial pada ujung masing-masing

    kapasitorkapasitor d. Energi yang tersimpan dalam susunan kapasitor

    11111Penyelesaian:

    pFpFCCCsub 61

    31111

    21

    +=+=a. pFC sub 2=b. q1 = q2 q = Csub.V = (2 x 10-12 F) (1000 V) = 2 nC

    c. V 667103102

    12

    9

    1

    11 ===

    FxCx

    CqV V 333

    106102

    12

    9

    2

    22 ===

    FxCx

    CqV

    Energi dalam d. g

    ( )( ) J 107.6V 66710221

    21 79

    111 === xCxVqW

    ( )( ) J 103.3V 33310221

    21 79

    222 === xCxVqW

    22

    ( ) J x1010J 10 x 3.3 6.7 -77 =+= subW

  • Heart Muscle Cells The cell wall acts as a capacitor since charges are separated The cell wall acts as a capacitor since charges are separated

    on the interior and exterior surfaces. The voltage is in the millivolt range.

    Molecules in the cell wall are polarized. The charge on the outside of the wall is on the order of 10-8of the wall is on the order of 10 8Coulomb.

    When the heart beats the wallWhen the heart beats, the wall depolarizes in a wave as shown in this picture. Here the wave proceeds from l f i h Af d l i i ileft to right. After depolarization is complete, the cell wall repolarizes.

    This cycle gives rise to an electrical signal that can be detected externally with an EKG (elektrokardiogram) machine.

  • EKG TracingEKG Tracing

    Th P i t ti f th h b t i ThThe P wave is contraction of the upper chambers or atria. The QRS is the ventricles. The wave proceeds from left to right and toward the front, then down to the left and toward the rear of the heart. The T wave is the re-polarization of the muscle in preparation for the next beat. Heart defects show up as variation

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